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                <h1 id="EverydayOneCat"><a href="#EverydayOneCat" class="headerlink" title="EverydayOneCat"></a>EverydayOneCat</h1><p>稍稍2 🌈</p>
<p><img src="https://pluto-1300780100.cos.ap-nanjing.myqcloud.com/img/5985ead40f8e8f383272f66951bab1656c5104aa.png@1036w.webp" alt="img" style="zoom:50%;"></p>
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<h1 id="自注意力机制"><a href="#自注意力机制" class="headerlink" title="自注意力机制"></a>自注意力机制</h1><h2 id="Vector-Set-as-Input"><a href="#Vector-Set-as-Input" class="headerlink" title="Vector Set as Input"></a>Vector Set as Input</h2><p>我们之前学习CNN时是将图像看作一个向量当作input，经过我们定义的网络模型输出。</p>
<p>那如果我们input一堆向量集呢（并且这些向量大小不一），这时候就需要我们接下来需要介绍的自注意力机制了。接下来通过几个例子来说明。</p>
<ol>
<li><p>比如我们输入一段话：this is a cat    显然每个单词的长短不一，并且每个词汇对应一个向量，所以输入是多个长短不一的向量。</p>
<p><img src="https://pluto-1300780100.cos.ap-nanjing.myqcloud.com/img/image-20221031144403156.png" alt="image-20221031144403156"></p>
<p>我们有两种方法将上面的话转成向量，一种是one-hot编码，但这种方法很明显能看出没有考虑每个词之间的联系，如cat和dog同为动物，但是两者没有丝毫联系，如果这样子当作input训练结果会很差劲，使用我们一般采用wrod embedding将上述一段单词转化为向量集。</p>
</li>
<li><p>一段声音序列也可以当作一堆向量集来作input</p>
<p><img src="https://pluto-1300780100.cos.ap-nanjing.myqcloud.com/img/image-20221031144809537.png" alt="image-20221031144809537"></p>
</li>
<li><p>图也是一堆向量的集合，如下图social network可以看作图，每个节点的信息可以当作一个向量，整个social network就是向量的集合。分子的结构也可以看做图，他们的结构也可以用一堆向量来表示。</p>
<p><img src="https://pluto-1300780100.cos.ap-nanjing.myqcloud.com/img/image-20221031144923909.png" alt="image-20221031144923909" style="zoom:80%;"></p>
<p><img src="https://pluto-1300780100.cos.ap-nanjing.myqcloud.com/img/image-20221031144940233.png" alt="image-20221031144940233" style="zoom:80%;"></p>
</li>
</ol>
<h2 id="What-is-the-output"><a href="#What-is-the-output" class="headerlink" title="What is the output"></a>What is the output</h2><p>上面讲到输入是一堆向量集，那么输出是什么呢，通常有以下三种情况：</p>
<ul>
<li><p>Each vector has a label——每个inpu向量对应一个输出output</p>
<p>比如我们的词性分析、社交网络判断商品是否推送等等</p>
<p><img src="https://pluto-1300780100.cos.ap-nanjing.myqcloud.com/img/image-20221031151849447.png" alt="image-20221031151849447" style="zoom:67%;"></p>
</li>
<li><p>The whole sequence has a label——一整个向量集的输入对应一个输出output标签</p>
<p>比如情感分析（分析一段话是乐观还是悲观）、通过分子结构判断是否有毒等等</p>
<p><img src="https://pluto-1300780100.cos.ap-nanjing.myqcloud.com/img/image-20221031152032831.png" alt="image-20221031152032831" style="zoom:80%;"></p>
</li>
<li><p>Model decides the number of labels itself——输出多少个标签由机器自己决定（也叫Seq2Seq）</p>
</li>
</ul>
<blockquote>
<p>总之引入自注意力机制的目的就是神经网络接收的输入是很多大小不一的向量，并且不同向量向量之间有一定的关系，但是实际训练的时候无法充分发挥这些输入之间的关系而导致模型训练结果效果极差。比如机器翻译问题(序列到序列的问题，机器自己决定多少个标签)，词性标注问题（一个向量对应一个标签)，语义分析问题(多个向量对应一个标签)等文字处理问题。</p>
</blockquote>
<p>我们本篇主要来介绍第一种情况，输入的一个向量对应输出的一个标签，也叫Sequence Labeling。</p>
<h2 id="引入self-attention"><a href="#引入self-attention" class="headerlink" title="引入self-attention"></a>引入self-attention</h2><p>在Sequence Labeling应用中，我们要求输入一段话进行词性分析：I saw a saw。</p>
<p><img src="https://pluto-1300780100.cos.ap-nanjing.myqcloud.com/img/image-20221031153142570.png" alt="image-20221031153142570"></p>
<p>如果是不考虑相关性直接丢入全连接层，那前一个saw词性肯定和后一个saw词性完全一样，但是我们人工知道，前面一个是动词，后面一个是名词。这时候就需要引入自注意力机制了。</p>
<p>针对全连接神经网络对于多个相关的输入无法建立起相关性的这个问题，通过自注意力机制来解决，它可以考虑一整个序列。自注意力机制实际上是想让机器注意到整个输入中不同部分之间的相关性。</p>
<h2 id="self-attention详解"><a href="#self-attention详解" class="headerlink" title="self-attention详解"></a>self-attention详解</h2><p>针对输入是一组向量，输出也是一组向量，输入长度为N（N可变化）的向量，输出同样为长度为N 的向量。</p>
<p><img src="https://pluto-1300780100.cos.ap-nanjing.myqcloud.com/img/image-20221031161431144.png" alt="image-20221031161431144" style="zoom:80%;"></p>
<p>如上图，我们input向量为a1、a2、a3、a4，输出b1、b2、b3、b4</p>
<p>我们以如何输出b1为例：</p>
<p><img src="https://pluto-1300780100.cos.ap-nanjing.myqcloud.com/img/image-20221031161307345.png" alt="image-20221031161307345" style="zoom:80%;"></p>
<p>首先，需要计算sequence中各向量与a1的关联程度，有下面两种方法</p>
<p><img src="https://pluto-1300780100.cos.ap-nanjing.myqcloud.com/img/image-20221031161614040.png" alt="image-20221031161614040" style="zoom:67%;"></p>
<p>其中α代表关联程度，在自注意力机制中，我们通常采用Dot-product方法来计算：两个向量作为输入，直接输出α，具体是输入的两个向量分别乘不同的矩阵$W^q$和$W^k$（$W^q$和$W^k$为权重矩阵，需要学习来更新参数），得到q,k,然后进行点乘即可得到α。α也就是表示两个向量之间的相关联程度。</p>
<p>可以计算每一个α(又称为attention score），q称为query，k称为key</p>
<p><img src="https://pluto-1300780100.cos.ap-nanjing.myqcloud.com/img/image-20221031162245244.png" alt="image-20221031162245244" style="zoom:80%;"></p>
<p> 另外，也可以计算a1和自己的关联性，再得到各向量与a1的相关程度之后，用softmax计算出一个attention distribution，这样就把相关程度归一化，通过数值就可以看出哪些向量是和a1最有关系。</p>
<p><img src="https://pluto-1300780100.cos.ap-nanjing.myqcloud.com/img/image-20221031162430305.png" alt="image-20221031162430305" style="zoom:80%;"></p>
<p> 下面需要根据 α′ 抽取sequence里重要的资讯， 先求v，v就是键值value，v和q、k计算方式相同，也是用输入a乘以权重矩阵W，得到v后，与对应的α′ 相乘，每一个v乘与α’后求和，得到输出b1。</p>
<p><img src="https://pluto-1300780100.cos.ap-nanjing.myqcloud.com/img/image-20221031163945566.png" alt="image-20221031163945566" style="zoom:80%;"></p>
<p>如果 a1 和 a2 关联性比较高， $a’_{12}$ 就比较大，那么得到的输出 b1 就可能比较接近 v2 ，即attention score决定了该vector在结果中占的分量</p>
<p>以此类推可以得到b2/b3/b4，要注意的是b1到b4不是依次产生的，是同时计算得到的。</p>
<h2 id="矩阵形式"><a href="#矩阵形式" class="headerlink" title="矩阵形式"></a>矩阵形式</h2><p><strong><em>Step</em></strong> <strong>1</strong>：q、k、v的矩阵形式生成</p>
<p>我们根据上面的描述可以写出q、k、v的计算公式</p>
<script type="math/tex; mode=display">
q^i = W^q * a^i \\
k^i = W^k * a^i \\
v^i = W^v * a^i</script><p>我们将输入向量$a1、a2、a3、a4$拼在一起，得到一个矩阵用$I$表示即$I=[a^1a^2a^3a^4]$</p>
<p>将上述公式写成矩阵形式：</p>
<script type="math/tex; mode=display">
K=W^kI \\
Q=W^qI \\
V=W^vI</script><p><img src="https://pluto-1300780100.cos.ap-nanjing.myqcloud.com/img/image-20221031171349987.png" alt="image-20221031171349987"></p>
<p><strong><em>Step</em></strong> <strong>2</strong>：利用得到的Q和K计算每两个输入向量之间的相关性，也就是计算attention的值α， α的计算方法有多种，通常采用点乘的方式。</p>
<p>前面提到将$q^1$和四个key向量$k^1,k^2,k^3,k^4$分别做点积，得到四个相关性数值$\alpha<em>{1,1},\alpha</em>{1,2},\alpha<em>{1,3},\alpha</em>{1,4}$。注意这里的向量都是列向量，所以点积可以写成</p>
<script type="math/tex; mode=display">
\alpha_{1,1}=q^1 \cdot k^1 =(k^1)^Tq^1 \\
\alpha_{1,2}=q^1 \cdot k^2 =(k^2)^Tq^1 \\
\alpha_{1,3}=q^1 \cdot k^3 =(k^3)^Tq^1 \\
\alpha_{1,4}=q^1 \cdot k^4 =(k^4)^Tq^1</script><p> 用矩阵计算表示上述计算过程为</p>
<script type="math/tex; mode=display">
\begin{bmatrix}\alpha_{1,1} \\\alpha_{1,2} \\\alpha_{1,3} \\\alpha_{1,4}\end{bmatrix}=\begin{bmatrix}(k^1)^T\\(k^2)^T\\(k^3)^T\\(k^4)^T\end{bmatrix}q^1=K^Tq^1</script><p>将$K^T$与$q^2、q^3、q^4$相乘可以得到相似的结果，即</p>
<script type="math/tex; mode=display">
A=\begin{bmatrix} \alpha_{1,1}&\alpha_{2,1} &\alpha_{3,1} &\alpha_{4,1} \\ \alpha_{1,2}&\alpha_{2,2} &\alpha_{3,2} &\alpha_{4,2} \\ \alpha_{1,3}&\alpha_{2,3} &\alpha_{3,3} &\alpha_{4,3} \\ \alpha_{1,4}&\alpha_{2,4} &\alpha_{3,4} &\alpha_{4,4} \end{bmatrix}=\begin{bmatrix}(k^1)^T\\(k^2)^T\\(k^3)^T\\(k^4)^T\end{bmatrix}[q^1q^2q^3q^4]=K^TQ</script><p>A矩阵通过softmax层归一化后得到A’。上述计算过程如下图所示。</p>
<p><img src="https://pluto-1300780100.cos.ap-nanjing.myqcloud.com/img/image-20221031172312712.png" alt="image-20221031172312712"></p>
<p><strong><em>Step 3：</em></strong>利用得到的A’和V，计算每个输入向量a对应的self-attention层的输出向量b：</p>
<script type="math/tex; mode=display">
O=[b^1b^2b^3b^4]=[v^1v^2v^3v^4]\begin{bmatrix} \alpha^{'}_{1,1}&\alpha^{'}_{2,1} &\alpha^{'}_{3,1} &\alpha^{'}_{4,1} \\ \alpha^{'}_{1,2}&\alpha^{'}_{2,2} &\alpha^{'}_{3,2} &\alpha^{'}_{4,2} \\ \alpha^{'}_{1,3}&\alpha^{'}_{2,3} &\alpha^{'}_{3,3} &\alpha^{'}_{4,3} \\ \alpha^{'}_{1,4}&\alpha^{'}_{2,4} &\alpha^{'}_{3,4} &\alpha^{'}_{4,4} \end{bmatrix}=VA'</script><p><img src="https://pluto-1300780100.cos.ap-nanjing.myqcloud.com/img/image-20221031172827182.png" alt="image-20221031172827182" style="zoom:80%;"></p>
<p>总结：</p>
<p><img src="https://pluto-1300780100.cos.ap-nanjing.myqcloud.com/img/image-20221031172929536.png" alt="image-20221031172929536" style="zoom:80%;"></p>
<p>其中矩阵$W^q、 W^k 、W^v$是需要学习的参数，自注意力机制看起来比较复杂，其实计算过程并不复杂。</p>
<h2 id="Multi-head-Self-attention"><a href="#Multi-head-Self-attention" class="headerlink" title="Multi-head Self-attention"></a>Multi-head Self-attention</h2><p>自注意力机制还有一个进阶版，叫多头自注意力机制（multi-head self-attention）。</p>
<p>为什么要多头呢？自注意力机制实质上是用过$q$向量去找相关的$k$向量，但是相关性可能有多种，一个只$q$能找到一种相关的$k$向量，因此就要引入多个$q$向量和$k$向量来捕捉多种相关性。多头自注意力机制很简单，设置多组矩阵$W^{q,i}、W^{k,i}、W^{v,i}$，每一组$W^{q,i}、W^{k,i}、W^{v,i}$只进行内部计算，得到相应的输出，$O^i$如下图所示。</p>
<p><img src="https://pluto-1300780100.cos.ap-nanjing.myqcloud.com/img/image-20221031173527231.png" alt="image-20221031173527231" style="zoom:80%;"></p>
<p>这只是两个head的例子，有多个head过程也一样，都是分开算b。</p>
<p>在得到不同的输出$O^i$后，再将其拼到一起，形成一个大的矩阵。</p>
<script type="math/tex; mode=display">
O=W^o\begin{bmatrix}O^1\\O^2 \end{bmatrix}</script><p>然后通过一个转换矩阵$W^o$将拼接的矩阵转换成原输出的长度的向量:</p>
<p><img src="https://pluto-1300780100.cos.ap-nanjing.myqcloud.com/img/image-20221031173700399.png" alt="image-20221031173700399"></p>
<p>因此，多头注意力机制要多一个参数矩阵，即$W^o$</p>
<h2 id="Positional-Encoding"><a href="#Positional-Encoding" class="headerlink" title="Positional Encoding"></a>Positional Encoding</h2><p>在训练self attention的时候，实际上对于位置的信息是缺失的，没有前后的区别，上面讲的a1,a2,a3不代表输入的顺序，只是指输入的向量数量，不像rnn，对于输入有明显的前后顺序，比如在翻译任务里面，对于“机器学习”，机器学习依次输入。而self-attention的输入是同时输入，输出也是同时产生然后输出的。</p>
<p>如何在Self-Attention里面体现位置信息呢？就是使用Positional Encoding</p>
<p>也就是新引入了一个位置向量$e^i$，非常简单，如下图所示：</p>
<p><img src="https://pluto-1300780100.cos.ap-nanjing.myqcloud.com/img/image-20221031173858174.png" alt="image-20221031173858174"></p>
<p>每一个位置设置一个vector,叫做positional vector，用$e^i$表示，不同的位置有一个专属的$e^i$。</p>
<p>如果$a^i$加上了$e^i$，就会体现出位置的信息，i是多少，位置就是多少。</p>
<p>vector长度是人为设定的，也可以从数据中训练出来。</p>
<h2 id="Self-attention-v-s-CNN"><a href="#Self-attention-v-s-CNN" class="headerlink" title="Self-attention v.s. CNN"></a>Self-attention v.s. CNN</h2><p>CNN只能考虑一部分输入，其实是简化版的Self-attention。</p>
<p><img src="https://pluto-1300780100.cos.ap-nanjing.myqcloud.com/img/image-20221031184619333.png" alt="image-20221031184619333"></p>
<p>在训练资料少的时候，CNN表现的更好。训练资料足够多的时候，self-attention表现得更好</p>
<p><img src="https://pluto-1300780100.cos.ap-nanjing.myqcloud.com/img/image-20221031184952579.png" alt="image-20221031184952579"></p>
<h2 id="Self-attention-v-s-RNN"><a href="#Self-attention-v-s-RNN" class="headerlink" title="Self-attention v.s. RNN"></a>Self-attention v.s. RNN</h2><p>Self-attention和RNN的主要区别在于：</p>
<ol>
<li><p>Self-attention可以考虑全部的输入，而RNN似乎只能考虑之前的输入（左边）。但是当使用双向RNN的时候可以避免这一问题。</p>
<p>比如，对于第一个RNN，只考虑了深蓝色的输入，绿色及绿色后面的输入不会考虑，而Self-Attention对于4个输入全部考虑</p>
<p><img src="https://pluto-1300780100.cos.ap-nanjing.myqcloud.com/img/69db4f64c89e47a2aa9dae93b6a4fbbe.png" alt="img" style="zoom:80%;"></p>
</li>
<li><p>Self-attention可以容易地考虑比较久之前的输入，而RNN的最早输入由于经过了很多层网络的处理变得较难考虑。</p>
<p>比如对于最后一个RNN的黄色输出，想要包含最开始的蓝色输入，必须保证蓝色输入在经过每层时信息都不丢失，但如果一个sequence很长，就很难保证。而Self-attention每个输出都和所有输入直接有关。</p>
<p><img src="https://pluto-1300780100.cos.ap-nanjing.myqcloud.com/img/a5d0ba187b3e42f2936ae3e6b1b93262.png" alt="img" style="zoom:80%;"></p>
</li>
<li><p>Self-attention可以并行计算，而RNN不同层之间具有先后顺序。</p>
</li>
</ol>
<h1 id="结语"><a href="#结语" class="headerlink" title="结语"></a>结语</h1><p>二次元yyds！！！</p>

                
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